Optimal. Leaf size=16 \[ 4+(4+x) \log (3)-(9+\log (x))^2 \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps
used = 5, number of rules used = 3, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {14, 45, 2338}
\begin {gather*} -\log ^2(x)-18 \log (x)+x \log (3) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 45
Rule 2338
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-18+x \log (3)}{x}-\frac {2 \log (x)}{x}\right ) \, dx\\ &=-\left (2 \int \frac {\log (x)}{x} \, dx\right )+\int \frac {-18+x \log (3)}{x} \, dx\\ &=-\log ^2(x)+\int \left (-\frac {18}{x}+\log (3)\right ) \, dx\\ &=x \log (3)-18 \log (x)-\log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} x \log (3)-18 \log (x)-\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.35, size = 16, normalized size = 1.00
method | result | size |
default | \(x \ln \left (3\right )-\ln \left (x \right )^{2}-18 \ln \left (x \right )\) | \(16\) |
norman | \(x \ln \left (3\right )-\ln \left (x \right )^{2}-18 \ln \left (x \right )\) | \(16\) |
risch | \(x \ln \left (3\right )-\ln \left (x \right )^{2}-18 \ln \left (x \right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 15, normalized size = 0.94 \begin {gather*} x \log \left (3\right ) - \log \left (x\right )^{2} - 18 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 0.94 \begin {gather*} x \log \left (3\right ) - \log \left (x\right )^{2} - 18 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.88 \begin {gather*} x \log {\left (3 \right )} - \log {\left (x \right )}^{2} - 18 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 0.94 \begin {gather*} x \log \left (3\right ) - \log \left (x\right )^{2} - 18 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.15, size = 15, normalized size = 0.94 \begin {gather*} -{\ln \left (x\right )}^2-18\,\ln \left (x\right )+x\,\ln \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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